Weyl’s theorem holds for algebraically hyponormal operators
نویسندگان
چکیده
منابع مشابه
Fuglede–putnam’s Theorem for W–hyponormal Operators
An asymmetric Fuglede-Putnam’s Theorem for w -hyponormal operators and dominant operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel. Mathematics subject classification (2010): 47B47, 47A30, 47B20.
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Let T be an algebraically paranormal operator acting on Hilbert space. We prove : (i) Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )); (ii) a-Browder’s theorem holds for f(S) for every S ≺ T and f ∈ H(σ(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T . Mathematics Subject Classification (2000). Primary 47A10, 4...
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If T or T ∗ is an algebraically k-quasiclass A operator acting on an infinite dimensional separable Hilbert space and F is an operator commuting with T , and there exists a positive integer n such that F has a finite rank, then we prove that Weyl’s theorem holds for f(T )+F for every f ∈ H(σ(T )), where H(σ(T )) denotes the set of all analytic functions in a neighborhood of σ(T ). Moreover, if ...
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A survey of the theory of k-hyponormal operators starts with the construction of a polynomially hyponormal operator which is not subnormal. This is achieved via a natural dictionary between positive functionals on specific convex cones of polynomials and linear bounded operators acting on a Hilbert space, with a distinguished cyclic vector. The class of unilateral weighted shifts provides an op...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05741-5